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Three charges are placed on the circumfe...

Three charges are placed on the circumference of a circle of radius d as shown in the figure. Find the electric field along x-axis at the centre of the circle :

Electric field due to `-4q vecE_(1) =(4kq)/d^(2)` electric field due to `+2q` and `-2q vecE_(23) = (4kq)/d^(2)`

A

`q/(4piepsilon_(0)d^(2))`

B

`(qsqrt(3))/(4piepsilon_(0)d^(2))`

C

`(qsqrt(3))/(piepsilon_(0)d^(2))`

D

`(qsqrt(3))/(2piepsilon_(0)d^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
Y-components of `vecE_(1)` and `vecE_(23)` are equal in magnitude and opposite in direction hence resultant electric field can be obtained by addition of jc-components only. `therefore` Resultant electric field
`E==(4kq)/d^(2)cos30^(@) + (4kq)/d^(2) cos(-30^(@))`
`=q/(piepsilon_(0)d^(2)) xx (2 xx sqrt(3))/2 =(qsqrt(3))/(piepsilon_(0)d^(2))`
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